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 # Q 4B


# Question is nothing but 1-D Heat Equation with heating at middle

# Solve by using finite difference method



import numpy as np

import matplotlib.pyplot as plt

from scipy.integrate import quad


x = np.linspace(0, 1, 101)

u = np.zeros(101)


u[0] = u[100] = 0       # Boundary Conditions

u[50] = 1               # Initial Condition


for t in range(100):

    for i in range(1,100):

        u[i] += (u[i+1] + u[i-1] -2*u[i])/4


plt.plot(x, u, 'r-', lw=3)

plt.xlabel("Length of rod")

plt.ylabel("Temperature (in reduced units)")

plt.title("Temperature Profile of Rod")

plt.show()

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